Brandon is 3 times as old as Umaima. Eight years ago, Brandon was 7 times as old as Umaima. How old is Umaima now?
Solution: We can use the given information to write down two equations that describe the ages of Brandon and Umaima. Let Brandon's current age be $b$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $b = 3u$ Eight years ago, Brandon was $b - 8$ years old, and Umaima was $u - 8$ years old. The information in the second sentence can be expressed in the following equation: $b - 8 = 7(u - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = 3u$ . Substituting this into our second equation, we get: $3u$ $-$ $8 = 7(u - 8)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $3 u - 8 = 7 u - 56$ Solving for $u$ , we get: $4 u = 48.$ $u = 12$.